Applications are open from October 5th to January 12th, 2024, for the PhD track in Economics.
PhD track program
The PhD track is a five-year program which offers training in top-level research to high-potential students aiming for an international career in leading academic institutions or companies.
For the first two years, candidates will be enrolled in a coursework program for which they would be awarded the master’s degree. Then, for the three remaining years, students will be enrolled in a dissertation phase for a PhD diploma.
PhD track in Economics
The program heavily relies on advanced quantitative methods for both theoretical and empirical analysis. During the first year, students take advanced core courses in microeconomics, macroeconomics, and econometrics. They also engage in research projects under the supervision of faculty and acquire a first hands-on contact with research. During the second year, students will follow advanced methodological courses, and specialize in subfields of economics. They will regularly spend time within the research centers (office space and IT facilities will be provided at CREST, students may also can work closely with faculty members as research assistants) and will be allocated an individual advisor among the program faculty. They will also regularly attend CREST research seminars, conduct a research project, and write a master’s dissertation under the supervision of a faculty member.
At the end of the second year, students who have achieved sufficiently good grades, have written a research proposal and found a potential PhD supervisor within CREST may progress to the dissertation period (three years) of the PhD program. Progress is conditional on securing funding and IP Paris and CREST will do their best to help candidates to obtain such funding (e.g., IP Paris but also Ecole polytechnique and ENSAE Paris provide a limited number of three-year doctoral fellowships).
Fields of excellence at our CREST research center (and HEC Paris research group), and potential areas of specialization, include:
- Econometric theory
- Environmental and development economics
- Game and decision theory
- Industrial organization and digital economics
- International economics
- Labor economics
- Public economics
Provide an advanced training in economics at the highest international level with a strong emphasis on advanced quantitative methods for both theoretical and empirical analyses.
Acquire the most important tools in microeconomics, macroeconomics, and econometrics through a complete core course training.
Specialize by selecting field and specialization courses in a variety of sub-areas of economics.
Conduct research in a stimulating environment
More information on the PhD track in Economics: https://www.ip-paris.fr/en/education/phd-track/phd-track-economics
More information on PhD tracks at IP Paris: https://www.ip-paris.fr/en/education/phd-track-applications-open-october-5th-january-12th-2024
|Thursday 07th April 2022
Monday 11th April 2022
Thursday 14th April 2022
|From 1:30 PM to 4:45 PM
From 1:30 PM to 4:45 PM
From 1:30 PM to 4:45 PM
This course will deal with the state-of-the-art in the theory of Pareto-optimal (re)insurance design under model uncertainty and/or non-Expected-Utility preferences, as well as provide an introduction to Pareto optimality in problems of peer-to-peer collaborative insurance. Specifically:
- We will start with some background material on the theory of decision-making under uncertainty, from the classical work on Expected-Utility Theory (EUT) of von Neumann and Morgenstern, Savage, and De Finetti, to the more recent work on ambiguity and probability distortions (Quiggin, Yaari, Schmeidler, Gilboa, Amarante, Maccheroni-Marinacci).
- We will cover some required mathematical tools, such as non-additive measure theory, probability distortions, Choquet integration, the theory of equimeasurable rearrangements, as well as risk measures, their properties, and their representations. We will pay special attention to distortion risk measures and spectral risk measures.
- We will then formally introduce a general model of the insurance market, following the work of Carlier and Dana , and study the existence and characterization of Pareto optima in this general setup. As a special case, we will consider the classical formulation of the optimal (re)insurance problem due to Arrow, in the framework of EUT, as well as more recent work extending Arrow’s setting to situations of belief heterogeneity between the two agents.
- We will then proceed to formulating several problems that extend the insurance model above to more general setting with non-EUT preferences, distortion risk measures, or situations of model uncertainty.
- Finally, we will go over a brief introduction to conditional mean risk sharing and peer-to-peer collaborative insurance.
|Thursday 06th January 2022
Tuesday 11th January 2022
Thursday 13th January 2022
Tuesday 18th January 2022
|From 2 PM to 4:30 PM
From 3 PM to 5:30 PM
From 2 PM to 4:30 PM
From 3 PM to 5:30 PM
This short course develops the fundamental limits of deep neural network learning from first principle by characterizing what is possible if no constraints on the learning algorithm and on the amount of training data are imposed. Concretely, we consider Kolmogorov-optimal approximation through deep neural networks with the guiding theme being a relation between the complexity of the function (class) to be approximated and the complexity of the approximating network in terms of connectivity and memory requirements for storing the network topology and the associated quantized weights. The theory we develop educes remarkable universality properties of deep networks. Specifically, deep networks are optimal approximants for markedly different function classes such as affine (i.e., wavelet-like) systems and Weyl-Heisenberg systems. This universality is afforded by a concurrent invariance property of deep networks to time-shifts, scalings, and frequency-shifts. In addition, deep networks provide exponential approximation accuracy—i.e., the approximation error decays exponentially in the number of non-zero weights in the network—of the multiplication operation, polynomials, sinusoidal functions, certain smooth functions, and even one-dimensional oscillatory textures and fractal functions such as the Weierstrass function, the latter two of which do not have previously known methods achieving exponential approximation accuracy. We also show that in the approximation of sufficiently smooth functions finite-width deep networks require strictly smaller connectivity than finite-depth wide networks.
The mathematical concepts forming the basis of this theory, namely metric entropy, linear and nonlinear approximation theory, best M-term approximation, and the theory of frames, will all be developed in the course.